# A reanalysis of a strong-flow gyrokinetic formalism

## Abstract

We reanalyse an arbitrary-wavelength gyrokinetic formalism [A. M. Dimits, Phys. Plasmas 17, 055901 (2010)], which orders only the vorticity to be small and allows strong, time-varying flows on medium and long wavelengths. We obtain a simpler gyrocentre Lagrangian up to second order. In addition, the gyrokinetic Poisson equation, derived either via variation of the system Lagrangian or explicit density calculation, is consistent with that of the weak-flow gyrokinetic formalism [T. S. Hahm, Phys. Fluids 31, 2670 (1988)] at all wavelengths in the weak flow limit. The reanalysed formalism has been numerically implemented as a particle-in-cell code. An iterative scheme is described which allows for numerical solution of this system of equations, given the implicit dependence of the Euler-Lagrange equations on the time derivative of the potential.

- Authors:

- Centre for Fusion, Space and Astrophysics, Physics Department, University of Warwick, Coventry CV4 7AL (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22408211

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 3; Other Information: (c) 2015 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; FLOW MODELS; ITERATIVE METHODS; LAGRANGE EQUATIONS; LAGRANGIAN FUNCTION; NUMERICAL SOLUTION; POISSON EQUATION; WAVELENGTHS

### Citation Formats

```
Sharma, A. Y., and McMillan, B. F..
```*A reanalysis of a strong-flow gyrokinetic formalism*. United States: N. p., 2015.
Web. doi:10.1063/1.4916129.

```
Sharma, A. Y., & McMillan, B. F..
```*A reanalysis of a strong-flow gyrokinetic formalism*. United States. doi:10.1063/1.4916129.

```
Sharma, A. Y., and McMillan, B. F.. Sun .
"A reanalysis of a strong-flow gyrokinetic formalism". United States.
doi:10.1063/1.4916129.
```

```
@article{osti_22408211,
```

title = {A reanalysis of a strong-flow gyrokinetic formalism},

author = {Sharma, A. Y. and McMillan, B. F.},

abstractNote = {We reanalyse an arbitrary-wavelength gyrokinetic formalism [A. M. Dimits, Phys. Plasmas 17, 055901 (2010)], which orders only the vorticity to be small and allows strong, time-varying flows on medium and long wavelengths. We obtain a simpler gyrocentre Lagrangian up to second order. In addition, the gyrokinetic Poisson equation, derived either via variation of the system Lagrangian or explicit density calculation, is consistent with that of the weak-flow gyrokinetic formalism [T. S. Hahm, Phys. Fluids 31, 2670 (1988)] at all wavelengths in the weak flow limit. The reanalysed formalism has been numerically implemented as a particle-in-cell code. An iterative scheme is described which allows for numerical solution of this system of equations, given the implicit dependence of the Euler-Lagrange equations on the time derivative of the potential.},

doi = {10.1063/1.4916129},

journal = {Physics of Plasmas},

number = 3,

volume = 22,

place = {United States},

year = {Sun Mar 15 00:00:00 EDT 2015},

month = {Sun Mar 15 00:00:00 EDT 2015}

}